{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "87bff5cd",
   "metadata": {},
   "outputs": [],
   "source": [
    "异常值处理方法"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "57f226e2",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np # 数据处理最重要的模块\n",
    "import pandas as pd # 数据处理最重要的模块\n",
    "import scipy.stats as stats # 统计模块\n",
    "import scipy\n",
    "# import pymysql  # 导入数据库模块\n",
    "\n",
    "from datetime import datetime # 时间模块\n",
    "import statsmodels.formula.api as smf  # OLS regression\n",
    "\n",
    "# import pyreadr # read RDS file\n",
    "\n",
    "from matplotlib import style\n",
    "import matplotlib.pyplot as plt  # 画图模块\n",
    "import matplotlib.dates as mdates\n",
    "\n",
    "\n",
    "from matplotlib.font_manager import FontProperties # 作图中文\n",
    "from pylab import mpl\n",
    "#mpl.rcParams['font.sans-serif'] = ['SimHei']\n",
    "#plt.rcParams['font.family'] = 'Times New Roman'\n",
    "\n",
    "\n",
    "#输出矢量图 渲染矢量图\n",
    "%matplotlib inline\n",
    "%config InlineBackend.figure_format = 'svg'\n",
    "\n",
    "from IPython.core.interactiveshell import InteractiveShell # jupyter运行输出的模块\n",
    "#显示每一个运行结果\n",
    "InteractiveShell.ast_node_interactivity = 'all'\n",
    "\n",
    "#设置行不限制数量\n",
    "#pd.set_option('display.max_rows',None)\n",
    "\n",
    "#设置列不限制数量\n",
    "pd.set_option('display.max_columns', None)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "453a9697",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "\n",
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       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Preclose</th>\n",
       "      <th>Open</th>\n",
       "      <th>Highest</th>\n",
       "      <th>Lowest</th>\n",
       "      <th>Close</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Day</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1990-12-19</th>\n",
       "      <td></td>\n",
       "      <td>96.050</td>\n",
       "      <td>99.980</td>\n",
       "      <td>95.790</td>\n",
       "      <td>99.980</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1990-12-20</th>\n",
       "      <td>99.98</td>\n",
       "      <td>104.300</td>\n",
       "      <td>104.390</td>\n",
       "      <td>99.980</td>\n",
       "      <td>104.390</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1990-12-21</th>\n",
       "      <td>104.39</td>\n",
       "      <td>109.070</td>\n",
       "      <td>109.130</td>\n",
       "      <td>103.730</td>\n",
       "      <td>109.130</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1990-12-24</th>\n",
       "      <td>109.13</td>\n",
       "      <td>113.570</td>\n",
       "      <td>114.550</td>\n",
       "      <td>109.130</td>\n",
       "      <td>114.550</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1990-12-25</th>\n",
       "      <td>114.55</td>\n",
       "      <td>120.090</td>\n",
       "      <td>120.250</td>\n",
       "      <td>114.550</td>\n",
       "      <td>120.250</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2025-08-25</th>\n",
       "      <td>3825.759</td>\n",
       "      <td>3848.163</td>\n",
       "      <td>3883.562</td>\n",
       "      <td>3839.972</td>\n",
       "      <td>3883.562</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2025-08-26</th>\n",
       "      <td>3883.562</td>\n",
       "      <td>3871.471</td>\n",
       "      <td>3888.599</td>\n",
       "      <td>3859.758</td>\n",
       "      <td>3868.382</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2025-08-27</th>\n",
       "      <td>3868.382</td>\n",
       "      <td>3869.612</td>\n",
       "      <td>3887.198</td>\n",
       "      <td>3800.350</td>\n",
       "      <td>3800.350</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2025-08-28</th>\n",
       "      <td>3800.35</td>\n",
       "      <td>3796.711</td>\n",
       "      <td>3845.087</td>\n",
       "      <td>3761.422</td>\n",
       "      <td>3843.597</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2025-08-29</th>\n",
       "      <td>3843.597</td>\n",
       "      <td>3842.823</td>\n",
       "      <td>3867.606</td>\n",
       "      <td>3839.206</td>\n",
       "      <td>3857.927</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>8473 rows × 5 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "            Preclose      Open   Highest    Lowest     Close\n",
       "Day                                                         \n",
       "1990-12-19              96.050    99.980    95.790    99.980\n",
       "1990-12-20     99.98   104.300   104.390    99.980   104.390\n",
       "1990-12-21    104.39   109.070   109.130   103.730   109.130\n",
       "1990-12-24    109.13   113.570   114.550   109.130   114.550\n",
       "1990-12-25    114.55   120.090   120.250   114.550   120.250\n",
       "...              ...       ...       ...       ...       ...\n",
       "2025-08-25  3825.759  3848.163  3883.562  3839.972  3883.562\n",
       "2025-08-26  3883.562  3871.471  3888.599  3859.758  3868.382\n",
       "2025-08-27  3868.382  3869.612  3887.198  3800.350  3800.350\n",
       "2025-08-28   3800.35  3796.711  3845.087  3761.422  3843.597\n",
       "2025-08-29  3843.597  3842.823  3867.606  3839.206  3857.927\n",
       "\n",
       "[8473 rows x 5 columns]"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data = pd.read_csv('000001.csv')\n",
    "data['Day'] = pd.to_datetime(data['Day'],format='%Y/%m/%d')\n",
    "data.set_index('Day', inplace = True)\n",
    "data.sort_values(by = ['Day'],axis=0, ascending=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "1e14d252",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Preclose</th>\n",
       "      <th>Open</th>\n",
       "      <th>Highest</th>\n",
       "      <th>Lowest</th>\n",
       "      <th>Close</th>\n",
       "      <th>Raw_return</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Day</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1995-01-03</th>\n",
       "      <td>647.870</td>\n",
       "      <td>637.720</td>\n",
       "      <td>647.710</td>\n",
       "      <td>630.530</td>\n",
       "      <td>639.880</td>\n",
       "      <td>-0.012333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1995-01-04</th>\n",
       "      <td>639.880</td>\n",
       "      <td>641.900</td>\n",
       "      <td>655.510</td>\n",
       "      <td>638.860</td>\n",
       "      <td>653.810</td>\n",
       "      <td>0.021770</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1995-01-05</th>\n",
       "      <td>653.810</td>\n",
       "      <td>655.380</td>\n",
       "      <td>657.520</td>\n",
       "      <td>645.810</td>\n",
       "      <td>646.890</td>\n",
       "      <td>-0.010584</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1995-01-06</th>\n",
       "      <td>646.890</td>\n",
       "      <td>642.750</td>\n",
       "      <td>643.890</td>\n",
       "      <td>636.330</td>\n",
       "      <td>640.760</td>\n",
       "      <td>-0.009476</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1995-01-09</th>\n",
       "      <td>640.760</td>\n",
       "      <td>637.520</td>\n",
       "      <td>637.550</td>\n",
       "      <td>625.040</td>\n",
       "      <td>626.000</td>\n",
       "      <td>-0.023035</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-09-24</th>\n",
       "      <td>2748.918</td>\n",
       "      <td>2770.754</td>\n",
       "      <td>2863.152</td>\n",
       "      <td>2761.372</td>\n",
       "      <td>2863.126</td>\n",
       "      <td>0.041547</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-09-25</th>\n",
       "      <td>2863.126</td>\n",
       "      <td>2901.419</td>\n",
       "      <td>2952.451</td>\n",
       "      <td>2889.048</td>\n",
       "      <td>2896.306</td>\n",
       "      <td>0.011589</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-09-26</th>\n",
       "      <td>2896.306</td>\n",
       "      <td>2893.745</td>\n",
       "      <td>3000.953</td>\n",
       "      <td>2889.014</td>\n",
       "      <td>3000.953</td>\n",
       "      <td>0.036131</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-09-27</th>\n",
       "      <td>3000.953</td>\n",
       "      <td>3049.103</td>\n",
       "      <td>3087.529</td>\n",
       "      <td>3017.445</td>\n",
       "      <td>3087.529</td>\n",
       "      <td>0.028850</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-09-30</th>\n",
       "      <td>3087.529</td>\n",
       "      <td>3194.722</td>\n",
       "      <td>3358.588</td>\n",
       "      <td>3153.697</td>\n",
       "      <td>3336.497</td>\n",
       "      <td>0.080637</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>7223 rows × 6 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "            Preclose      Open   Highest    Lowest     Close  Raw_return\n",
       "Day                                                                     \n",
       "1995-01-03   647.870   637.720   647.710   630.530   639.880   -0.012333\n",
       "1995-01-04   639.880   641.900   655.510   638.860   653.810    0.021770\n",
       "1995-01-05   653.810   655.380   657.520   645.810   646.890   -0.010584\n",
       "1995-01-06   646.890   642.750   643.890   636.330   640.760   -0.009476\n",
       "1995-01-09   640.760   637.520   637.550   625.040   626.000   -0.023035\n",
       "...              ...       ...       ...       ...       ...         ...\n",
       "2024-09-24  2748.918  2770.754  2863.152  2761.372  2863.126    0.041547\n",
       "2024-09-25  2863.126  2901.419  2952.451  2889.048  2896.306    0.011589\n",
       "2024-09-26  2896.306  2893.745  3000.953  2889.014  3000.953    0.036131\n",
       "2024-09-27  3000.953  3049.103  3087.529  3017.445  3087.529    0.028850\n",
       "2024-09-30  3087.529  3194.722  3358.588  3153.697  3336.497    0.080637\n",
       "\n",
       "[7223 rows x 6 columns]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data_new = data['1995-01':'2024-09'].copy()\n",
    "data_new['Close'] = pd.to_numeric(data_new['Close'])\n",
    "data_new['Preclose'] = pd.to_numeric(data_new['Preclose'])\n",
    "# 计算000001上证指数日收益率 两种：\n",
    "data_new['Raw_return'] = data_new['Close'] / data_new['Preclose'] - 1\n",
    "data_new"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "46b000fa",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Raw_return</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Day</th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1995-01-31</th>\n",
       "      <td>-0.131631</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1995-02-28</th>\n",
       "      <td>-0.023694</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1995-03-31</th>\n",
       "      <td>0.177803</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1995-04-30</th>\n",
       "      <td>-0.103552</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1995-05-31</th>\n",
       "      <td>0.207922</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-05-31</th>\n",
       "      <td>-0.005801</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-06-30</th>\n",
       "      <td>-0.038684</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-07-31</th>\n",
       "      <td>-0.009656</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-08-31</th>\n",
       "      <td>-0.032849</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-09-30</th>\n",
       "      <td>0.173908</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>357 rows × 1 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "            Raw_return\n",
       "Day                   \n",
       "1995-01-31   -0.131631\n",
       "1995-02-28   -0.023694\n",
       "1995-03-31    0.177803\n",
       "1995-04-30   -0.103552\n",
       "1995-05-31    0.207922\n",
       "...                ...\n",
       "2024-05-31   -0.005801\n",
       "2024-06-30   -0.038684\n",
       "2024-07-31   -0.009656\n",
       "2024-08-31   -0.032849\n",
       "2024-09-30    0.173908\n",
       "\n",
       "[357 rows x 1 columns]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Month_data = data_new.resample('ME')['Raw_return'].apply(lambda x: (1+x).prod()-1).to_frame()\n",
    "Month_data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "5aa95448",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Raw_return</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Day</th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1995-03-31</th>\n",
       "      <td>-0.001466</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1995-06-30</th>\n",
       "      <td>-0.025258</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1995-09-30</th>\n",
       "      <td>0.145660</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1995-12-31</th>\n",
       "      <td>-0.231358</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1996-03-31</th>\n",
       "      <td>0.001981</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2023-09-30</th>\n",
       "      <td>-0.028603</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2023-12-31</th>\n",
       "      <td>-0.043575</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-03-31</th>\n",
       "      <td>0.022263</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-06-30</th>\n",
       "      <td>-0.024255</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-09-30</th>\n",
       "      <td>0.124383</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>119 rows × 1 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "            Raw_return\n",
       "Day                   \n",
       "1995-03-31   -0.001466\n",
       "1995-06-30   -0.025258\n",
       "1995-09-30    0.145660\n",
       "1995-12-31   -0.231358\n",
       "1996-03-31    0.001981\n",
       "...                ...\n",
       "2023-09-30   -0.028603\n",
       "2023-12-31   -0.043575\n",
       "2024-03-31    0.022263\n",
       "2024-06-30   -0.024255\n",
       "2024-09-30    0.124383\n",
       "\n",
       "[119 rows x 1 columns]"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Quarter_data = data_new.resample('QE')['Raw_return'].apply(lambda x: (1+x).prod()-1).to_frame()\n",
    "Quarter_data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "2645033c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Raw_return</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Day</th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1995-12-31</th>\n",
       "      <td>-0.142899</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1996-12-31</th>\n",
       "      <td>0.651425</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1997-12-31</th>\n",
       "      <td>0.302153</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1998-12-31</th>\n",
       "      <td>-0.039695</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1999-12-31</th>\n",
       "      <td>0.191750</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2000-12-31</th>\n",
       "      <td>0.517277</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2001-12-31</th>\n",
       "      <td>-0.206180</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2002-12-31</th>\n",
       "      <td>-0.175167</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2003-12-31</th>\n",
       "      <td>0.102670</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2004-12-31</th>\n",
       "      <td>-0.153997</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2005-12-31</th>\n",
       "      <td>-0.083253</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2006-12-31</th>\n",
       "      <td>1.304334</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2007-12-31</th>\n",
       "      <td>0.966593</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2008-12-31</th>\n",
       "      <td>-0.653941</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2009-12-31</th>\n",
       "      <td>0.799825</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2010-12-31</th>\n",
       "      <td>-0.143131</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2011-12-31</th>\n",
       "      <td>-0.216753</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2012-12-31</th>\n",
       "      <td>0.031695</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2013-12-31</th>\n",
       "      <td>-0.067493</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2014-12-31</th>\n",
       "      <td>0.528691</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2015-12-31</th>\n",
       "      <td>0.094136</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016-12-31</th>\n",
       "      <td>-0.123062</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-12-31</th>\n",
       "      <td>0.065578</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2018-12-31</th>\n",
       "      <td>-0.245911</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2019-12-31</th>\n",
       "      <td>0.223032</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2020-12-31</th>\n",
       "      <td>0.138667</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2021-12-31</th>\n",
       "      <td>0.048001</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2022-12-31</th>\n",
       "      <td>-0.151250</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2023-12-31</th>\n",
       "      <td>-0.037007</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-12-31</th>\n",
       "      <td>0.121536</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            Raw_return\n",
       "Day                   \n",
       "1995-12-31   -0.142899\n",
       "1996-12-31    0.651425\n",
       "1997-12-31    0.302153\n",
       "1998-12-31   -0.039695\n",
       "1999-12-31    0.191750\n",
       "2000-12-31    0.517277\n",
       "2001-12-31   -0.206180\n",
       "2002-12-31   -0.175167\n",
       "2003-12-31    0.102670\n",
       "2004-12-31   -0.153997\n",
       "2005-12-31   -0.083253\n",
       "2006-12-31    1.304334\n",
       "2007-12-31    0.966593\n",
       "2008-12-31   -0.653941\n",
       "2009-12-31    0.799825\n",
       "2010-12-31   -0.143131\n",
       "2011-12-31   -0.216753\n",
       "2012-12-31    0.031695\n",
       "2013-12-31   -0.067493\n",
       "2014-12-31    0.528691\n",
       "2015-12-31    0.094136\n",
       "2016-12-31   -0.123062\n",
       "2017-12-31    0.065578\n",
       "2018-12-31   -0.245911\n",
       "2019-12-31    0.223032\n",
       "2020-12-31    0.138667\n",
       "2021-12-31    0.048001\n",
       "2022-12-31   -0.151250\n",
       "2023-12-31   -0.037007\n",
       "2024-12-31    0.121536"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Year_data = data_new.resample('YE')['Raw_return'].apply(lambda x: (1+x).prod()-1).to_frame()\n",
    "Year_data"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "219e032d",
   "metadata": {},
   "source": [
    "固定比例法"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "242a95b7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "np.float64(0.2744642236184609)"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "np.float64(-0.2463139446677537)"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Month_data['2000-01':'2024-09']['Raw_return'].max()\n",
    "Month_data['2000-01':'2024-09']['Raw_return'].min()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "ec83d3ac",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "      <th>Raw_return</th>\n",
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       "      <th>Day</th>\n",
       "      <th></th>\n",
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       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2000-01-31</th>\n",
       "      <td>0.123242</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2000-02-29</th>\n",
       "      <td>0.116990</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2000-03-31</th>\n",
       "      <td>0.049948</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2000-04-30</th>\n",
       "      <td>0.020053</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2000-05-31</th>\n",
       "      <td>0.031710</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-05-31</th>\n",
       "      <td>-0.005801</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-06-30</th>\n",
       "      <td>-0.038684</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-07-31</th>\n",
       "      <td>-0.009656</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-08-31</th>\n",
       "      <td>-0.032849</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-09-30</th>\n",
       "      <td>0.173908</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>297 rows × 1 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "            Raw_return\n",
       "Day                   \n",
       "2000-01-31    0.123242\n",
       "2000-02-29    0.116990\n",
       "2000-03-31    0.049948\n",
       "2000-04-30    0.020053\n",
       "2000-05-31    0.031710\n",
       "...                ...\n",
       "2024-05-31   -0.005801\n",
       "2024-06-30   -0.038684\n",
       "2024-07-31   -0.009656\n",
       "2024-08-31   -0.032849\n",
       "2024-09-30    0.173908\n",
       "\n",
       "[297 rows x 1 columns]"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Month_data_fix = Month_data['2000-01':'2024-09'].copy()\n",
    "Month_data_fix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "361361b6",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "      <th>2000-01-31</th>\n",
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       "      <th>2000-02-29</th>\n",
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       "      <th>2000-03-31</th>\n",
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       "    <tr>\n",
       "      <th>2000-04-30</th>\n",
       "      <td>0.020053</td>\n",
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       "    <tr>\n",
       "      <th>2000-05-31</th>\n",
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       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
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       "    <tr>\n",
       "      <th>2024-05-31</th>\n",
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       "    <tr>\n",
       "      <th>2024-06-30</th>\n",
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       "    <tr>\n",
       "      <th>2024-07-31</th>\n",
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       "    <tr>\n",
       "      <th>2024-08-31</th>\n",
       "      <td>-0.032849</td>\n",
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       "    <tr>\n",
       "      <th>2024-09-30</th>\n",
       "      <td>0.173908</td>\n",
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       "  </tbody>\n",
       "</table>\n",
       "<p>297 rows × 1 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "            Raw_return\n",
       "Day                   \n",
       "2000-01-31    0.123242\n",
       "2000-02-29    0.116990\n",
       "2000-03-31    0.049948\n",
       "2000-04-30    0.020053\n",
       "2000-05-31    0.031710\n",
       "...                ...\n",
       "2024-05-31   -0.005801\n",
       "2024-06-30   -0.038684\n",
       "2024-07-31   -0.009656\n",
       "2024-08-31   -0.032849\n",
       "2024-09-30    0.173908\n",
       "\n",
       "[297 rows x 1 columns]"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Month_data_fix[Month_data_fix['Raw_return'] > Month_data_fix['Raw_return'].quantile(\n",
    "    0.99)] = Month_data_fix['Raw_return'].quantile(0.99)\n",
    "Month_data_fix[Month_data_fix['Raw_return'] < Month_data_fix['Raw_return'].quantile(\n",
    "    0.01)] = Month_data_fix['Raw_return'].quantile(0.01)\n",
    "Month_data_fix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "e977df1f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "count    297.000000\n",
       "mean       0.005530\n",
       "std        0.070834\n",
       "min       -0.246314\n",
       "25%       -0.037767\n",
       "50%        0.004454\n",
       "75%        0.043145\n",
       "max        0.274464\n",
       "Name: Raw_return, dtype: float64"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "count    297.000000\n",
       "mean       0.005365\n",
       "std        0.068627\n",
       "min       -0.203684\n",
       "25%       -0.037767\n",
       "50%        0.004454\n",
       "75%        0.043145\n",
       "max        0.185927\n",
       "Name: Raw_return, dtype: float64"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Month_data['2000-01':'2024-09']['Raw_return'].describe().round(8)\n",
    "Month_data_fix['2000-01':'2024-09']['Raw_return'].describe().round(8)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "811dfb48",
   "metadata": {},
   "source": [
    "均值标准差法"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "916dd488",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "      <th>2024-05-31</th>\n",
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       "      <th>2024-08-31</th>\n",
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      ],
      "text/plain": [
       "            Raw_return\n",
       "Day                   \n",
       "2000-01-31    0.123242\n",
       "2000-02-29    0.116990\n",
       "2000-03-31    0.049948\n",
       "2000-04-30    0.020053\n",
       "2000-05-31    0.031710\n",
       "...                ...\n",
       "2024-05-31   -0.005801\n",
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       "2024-09-30    0.173908\n",
       "\n",
       "[297 rows x 1 columns]"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Month_data_ms = Month_data['2000-01':'2024-09'].copy()\n",
    "\n",
    "Month_data_ms[Month_data_ms['Raw_return'] >= Month_data_ms['Raw_return'].mean() +\n",
    "         3 * Month_data_ms['Raw_return'].std()] = Month_data_ms['Raw_return'].mean(\n",
    "         ) + 3 * Month_data_ms['Raw_return'].std()\n",
    "\n",
    "Month_data_ms[Month_data_ms['Raw_return'] <= Month_data_ms['Raw_return'].mean() -\n",
    "         3 * Month_data_ms['Raw_return'].std()] = Month_data_ms['Raw_return'].mean(\n",
    "         ) - 3 * Month_data_ms['Raw_return'].std()\n",
    "Month_data_ms"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "ac92191a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "count    297.000000\n",
       "mean       0.005530\n",
       "std        0.070834\n",
       "min       -0.246314\n",
       "25%       -0.037767\n",
       "50%        0.004454\n",
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       "Name: Raw_return, dtype: float64"
      ]
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     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
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    {
     "data": {
      "text/plain": [
       "count    297.000000\n",
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     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
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   "source": [
    "Month_data['2000-01':'2024-09']['Raw_return'].describe().round(8)\n",
    "Month_data_ms['2000-01':'2024-09']['Raw_return'].describe().round(8)"
   ]
  },
  {
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   "id": "f320cc7c",
   "metadata": {},
   "source": [
    "MAD法"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "a2431737",
   "metadata": {},
   "outputs": [
    {
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       "      <th></th>\n",
       "      <th>Raw_return</th>\n",
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       "      <th>2000-01-31</th>\n",
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       "    <tr>\n",
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       "            Raw_return\n",
       "Day                   \n",
       "2000-01-31    0.123242\n",
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       "2000-03-31    0.049948\n",
       "2000-04-30    0.020053\n",
       "2000-05-31    0.031710\n",
       "...                ...\n",
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       "\n",
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    "Month_data_median = Month_data['2000-01':'2024-09'].copy()\n",
    "\n",
    "median = np.median(Month_data_median['Raw_return'])\n",
    "MAD = np.mean(abs(Month_data_median['Raw_return'] - median))\n",
    "\n",
    "Month_data_median[Month_data_median['Raw_return'] >= 3 * MAD + median] = 3 * MAD + median\n",
    "Month_data_median[Month_data_median['Raw_return'] <= -3 * MAD + median] = -3 * MAD + median\n",
    "\n",
    "Month_data_median"
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  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "79b85408",
   "metadata": {},
   "outputs": [
    {
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      "text/plain": [
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       "std        0.070834\n",
       "min       -0.246314\n",
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       "50%        0.004454\n",
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       "max        0.274464\n",
       "Name: Raw_return, dtype: float64"
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     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
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    {
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     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
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   "source": [
    "Month_data['2000-01':'2024-09']['Raw_return'].describe().round(8)\n",
    "Month_data_median['2000-01':'2024-09']['Raw_return'].describe().round(8)"
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  {
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   "id": "c0b88e7a",
   "metadata": {},
   "source": [
    "参数假设检验"
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  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "5ee2af2c",
   "metadata": {},
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       "</svg>\n"
      ],
      "text/plain": [
       "<Figure size 800x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize = (8,4))\n",
    "\n",
    "ax.plot('Raw_return', # 图片数据\n",
    "'.-', # 图片类型,\n",
    "color = 'blue', # 图片颜色\n",
    "label = 'Monthly Return', # 图片标签\n",
    "linewidth = 2, # 图片线宽\n",
    "data = Month_data['2000-01':]) # 图片数据来源\n",
    "ax.set_title(\"China's stock market\") # 图片标题\n",
    "ax.set_ylabel('Return') # 图片y轴标签\n",
    "ax.set_xlabel('Year') # 图片x轴标签\n",
    "\n",
    "# 添加一条y=0的参考线\n",
    "plt.axhline(y=0, color='blue', linewidth=2)\n",
    "# plt.axhline(y=0.005546421267857977, color='green', linewidth=2)\n",
    "\n",
    "# 设置x轴的日期显示格式\n",
    "data_format = mdates.DateFormatter('%Y')\n",
    "ax.xaxis.set_major_formatter(data_format)\n",
    "ax.xaxis.set_major_locator(mdates.YearLocator())\n",
    "\n",
    "# 转置x轴的日期显示格式\n",
    "plt.xticks(rotation = 90)\n",
    "\n",
    "# 添加图例\n",
    "plt.legend(loc='upper right',fontsize = 8)\n",
    "plt.show();"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1343ce94",
   "metadata": {},
   "source": [
    "单个总体均值的假设检验"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "91467cff",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "np.float64(0.005529580266316066)"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Month_data['2000-01':'2024-09']['Raw_return'].mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "7ba7ce8e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "TtestResult(statistic=np.float64(1.8515511117890133), pvalue=np.float64(0.06491819809694584), df=np.int64(356))"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stats.ttest_1samp(Month_data['1995-01':'2024-09']['Raw_return'],0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "5584c74b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "TtestResult(statistic=np.float64(1.3453254245037998), pvalue=np.float64(0.17954988199447114), df=np.int64(296))"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stats.ttest_1samp(Month_data['2000-01':'2024-09']['Raw_return'],0)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "af662ca3",
   "metadata": {},
   "source": [
    "Q"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "448bffa1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "np.float64(83.2)"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 学生的分数数79 79 79 79 100\n",
    "# 均值是多少\n",
    "data = [79,79,79,79,100]\n",
    "np.mean(data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "0dadd51c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "TtestResult(statistic=np.float64(0.7619047619047625), pvalue=np.float64(0.4885651283802229), df=np.int64(4))"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# t.test data\n",
    "stats.ttest_1samp(data,80)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "5b757ad0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['Solarize_Light2',\n",
       " '_classic_test_patch',\n",
       " '_mpl-gallery',\n",
       " '_mpl-gallery-nogrid',\n",
       " 'bmh',\n",
       " 'classic',\n",
       " 'dark_background',\n",
       " 'fast',\n",
       " 'fivethirtyeight',\n",
       " 'ggplot',\n",
       " 'grayscale',\n",
       " 'petroff10',\n",
       " 'seaborn-v0_8',\n",
       " 'seaborn-v0_8-bright',\n",
       " 'seaborn-v0_8-colorblind',\n",
       " 'seaborn-v0_8-dark',\n",
       " 'seaborn-v0_8-dark-palette',\n",
       " 'seaborn-v0_8-darkgrid',\n",
       " 'seaborn-v0_8-deep',\n",
       " 'seaborn-v0_8-muted',\n",
       " 'seaborn-v0_8-notebook',\n",
       " 'seaborn-v0_8-paper',\n",
       " 'seaborn-v0_8-pastel',\n",
       " 'seaborn-v0_8-poster',\n",
       " 'seaborn-v0_8-talk',\n",
       " 'seaborn-v0_8-ticks',\n",
       " 'seaborn-v0_8-white',\n",
       " 'seaborn-v0_8-whitegrid',\n",
       " 'tableau-colorblind10']"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "style.available"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "30a31071",
   "metadata": {},
   "outputs": [
    {
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    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import scipy.stats as stats\n",
    "\n",
    "# 设置参数\n",
    "alpha = 0.05  # 显著性水平\n",
    "df = 100  # 自由度，假设样本量为101\n",
    "t_crit = stats.t.ppf(1 - alpha / 2, df)  # 双侧检验临界值\n",
    "\n",
    "# 生成 t 分布的 x 轴数据\n",
    "x = np.linspace(-4, 4, 1000) # 生成 -4 到 4 之间的 1000 个数据\n",
    "y = stats.t.pdf(x, df) # 计算 t 分布的概率密度函数\n",
    "\n",
    "# 绘制 t 分布曲线\n",
    "plt.figure(figsize=(12, 6)) # 设置图形大小\n",
    "plt.style.use('ggplot') # 设置风格\n",
    "plt.plot(x, y, label=f't-distribution (df={df})', color='blue') # 绘制 t 分布曲线\n",
    "\n",
    "# 填充拒绝原假设区域\n",
    "plt.fill_between(x, 0, y, where=(x >= t_crit) | (x <= -t_crit), color='red', alpha=0.7, label='Rejection region')\n",
    "\n",
    "# 标出 t 临界值\n",
    "plt.axvline(t_crit, color='red', linestyle='--', label=f'Critical value = {t_crit:.2f}') # 标出临界值\n",
    "plt.axvline(-t_crit, color='red', linestyle='--') # 标出临界值\n",
    "\n",
    "# 假设计算出的 t 值 (例如 t = 2.1)\n",
    "t_value = 2.1\n",
    "plt.axvline(t_value, color='green', linestyle='-', label=f't-value = {t_value}')\n",
    "\n",
    "# 图形标注\n",
    "plt.title('t-distribution with Rejection Regions and t-value')\n",
    "plt.xlabel('t-value')\n",
    "plt.ylabel('Probability Density')\n",
    "plt.legend()\n",
    "\n",
    "# 显示图形\n",
    "plt.show();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "c1826f75",
   "metadata": {},
   "outputs": [
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   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# 设置参数\n",
    "num_trials = 10000  # 总实验次数\n",
    "num_samples = 1000  # 每次实验的样本大小\n",
    "results = []  # 存储每次实验的均值\n",
    "\n",
    "# 模拟实验\n",
    "for _ in range(num_trials):\n",
    "    # 抛掷硬币，0代表正面，1代表反面\n",
    "    samples = np.random.binomial(n=1, p=0.5, size=num_samples) # 二项分布\n",
    "    results.append(np.mean(samples))  # 计算均值并存储\n",
    "\n",
    "# 计算总体均值\n",
    "theoretical_mean = 0.5  # 理论均值（正面概率）\n",
    "\n",
    "# 绘制结果\n",
    "plt.figure(figsize=(10, 6))\n",
    "plt.plot(np.arange(1, num_trials + 1), results, label='Sample Mean', color='blue', alpha=0.5)\n",
    "plt.axhline(y=theoretical_mean, color='red', linestyle='--', label='Theoretical Mean (0.5)')\n",
    "plt.title('Law of Large Numbers: Sample Mean vs. Theoretical Mean')\n",
    "plt.xlabel('Number of Trials')\n",
    "plt.ylabel('Sample Mean')\n",
    "plt.legend()\n",
    "plt.grid(True)\n",
    "plt.ylim(0, 1)  # 限制 y 轴范围\n",
    "plt.show();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "a19e7a5c",
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   "source": [
    "import seaborn as sns\n",
    "\n",
    "# 设置参数\n",
    "num_samples = 1000  # 每次抽样的样本大小\n",
    "num_trials = 1000   # 抽样的次数\n",
    "sample_means = []   # 存储样本均值\n",
    "\n",
    "# 从非正态分布（例如均匀分布）中抽样\n",
    "for _ in range(num_trials):\n",
    "    samples = np.random.uniform(low=-1, high=1, size=num_samples)  # 生成均匀分布样本\n",
    "    sample_means.append(np.mean(samples))  # 计算均值并存储\n",
    "\n",
    "# 绘制结果\n",
    "plt.figure(figsize=(12, 6))\n",
    "\n",
    "# 绘制样本均值的分布\n",
    "sns.histplot(sample_means, bins=30, kde=True, color='blue', stat='density', label='Sample Means')\n",
    "\n",
    "# 绘制标准正态分布\n",
    "mu = np.mean(sample_means)\n",
    "sigma = np.std(sample_means)\n",
    "x = np.linspace(mu - 4*sigma, mu + 4*sigma, 100)\n",
    "plt.plot(x, stats.norm.pdf(x, mu, sigma), color='red', linestyle='--', label='Normal Distribution')\n",
    "\n",
    "# 图形标注\n",
    "plt.title('Demonstration of the Central Limit Theorem')\n",
    "plt.xlabel('Sample Means')\n",
    "plt.ylabel('Density')\n",
    "plt.legend()\n",
    "plt.grid(True)\n",
    "plt.show();"
   ]
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